(1) Field of the Invention
This invention relates to a method and apparatus for deducing positions, orientations and sizes of bioelectric current sources.
(2) Description of the Related Art
A stimulus given to a living body breaks polarization across cell membranes and generates bioelectric currents. Such bioelectric currents take place in the brain and the heart, and are recorded as an electro-oencephalogram or an electrocardiogram. The magnetic fields formed by such bioelectric currents are recorded as a magnetoencephalogram or a magnetocardiogram.
In recent years, a senor using a SQUID (Super-conducting Quantum Interface Device) has been developed as a device for measuring minute magnetic fields in the living body. This sensor may be placed outside the head to measure, in a painless and harmless way, minute magnetic fields formed by current dipoles (hereinafter simply called current sources also) which are bioelectric current sources occurring in the brain. The positions, orientations and sizes of the current sources relating to a lesion are deduced from the magnetic field data thus gained. The current sources deduced are superposed on sectional images obtained from a radiographic CT apparatus or MRI apparatus, to determine a physical position and other features of a disease or the like.
One example of conventional methods for deducing current sources uses a least norm method (see, for example, W. H. Kullmann, K. D. Jandt, K. Rehm, H. A. Schlitte, W. J. Dallas and W. E. Smith, Advances in Biomagnetism, pp. 571-574, Plenum Press, New York, 1989).
The conventional method of deducing current sources using the least norm method will be described hereinafter with reference to FIG. 1.
As shown in FIG. 1, a multichannel SQUID sensor 1 is disposed adjacent an examinee M. The multichannel SQUID sensor 1 has a multiplicity of magnetic sensors (pickup coils) S1 to Sm immersed in a coolant such as liquid nitrogen within a vessel called a Dewar.
On the other hand, a multiplicity of lattice points "1" to "n" are set in a region to be diagnosed, e.g. the brain, of the examinee M. Unknown current sources (current dipoles) are assumed for the respective lattice points, which are expressed by three-dimensional vectors VPj (j=1 to n). Then, the respective magnetic sensors S1 to Sm of the SQUID sensor 1 detect magnetic fields B1 to Bm which are expressed by the following equations (1): ##EQU1##
In the equations (1), VPj=(Pjx, Pjy, Pjz), and .alpha.ij=(.alpha.ijx, .alpha.ijy, .alpha.ijz). .alpha.ij is a known coefficient representing intensity of a magnetic field detected in the position of each magnetic sensor S1 to Sm, where the current sources of unit sizes in X, Y and Z directions are arranged on the lattice points.
If [B]=(B1, B2, . . . Bm), and [P]=(P1x, P1y, P1z, P2x, P2y, P2z, . . . Pnx, Pny, Pnz), then the equations (1) are rewritten as the following linear relationship (2): EQU [B]=A[P] (2)
In the equation (2), A is a matrix having 3n.times.m elements expressed by the following equation (3): ##EQU2##
If the inverse matrix of A is expressed by A.sup.-, [P] is expressed by the following equation (4): EQU [P]=A.sup.- [B] (4)
The least norm method is based on the premise that the number of unknowns 3n (where the sizes in X, Y and Z directions of the current sources assumed for the respective lattice points are taken into account) is greater than the number of equations m (the number of magnetic sensors S1 to Sm). This method finds solutions for current sources [P] by applying the condition that norm .vertline.[P].vertline. of current sources [P] is minimized. The solutions could be obtained uniformly by equalizing the number of equations m and the number of unknowns 3n, but such solutions would be very unstable. For this reason, the least norm method is employed.
By applying the condition that norm .vertline.[P].vertline. of current sources [P] is minimized, the above equation (4) is rewritten as the following equation (5): EQU [P]=A.sup.+ [B] (5)
where A.sup.+ is a general inverse matrix expressed by the following equation (6): EQU A.sup.+ =A.sup.t (AA.sup.t).sup.-1 ( 6) PA1 where A.sup.t is a transposed matrix of A. PA1 a magnetic field measuring step for measuring minute magnetic fields formed by the bioelectric current sources in a region under examination of an examinee, with a plurality of magnetic sensors arranged adjacent the region under examination; PA1 a lattice point setting step for setting a plurality of lattice points in the region under examination; PA1 a current source computing step for deriving physical quantities of the current sources by solving a relational expression of unknown current sources at the lattice points and field data provided by the magnetic sensors, with a condition added thereto to minimize a norm of a vector having the current source at each of the lattice points; PA1 a lattice point rearranging step for moving the lattice points toward a lattice point having a large current value among the current sources computed; PA1 a checking step for checking whether a minimum distance among the lattice points having been moved is below a predetermined value; and PA1 a current source identifying step for repeating the current source computing step to the checking step for the lattice points having been removed, when the minimum distance exceeds the predetermined value, and regarding as a true current source the current source corresponding to a magnetic field occurring when the minimum distance is determined to be below the predetermined value at the checking step. PA1 a magnetic field measuring step for measuring minute magnetic fields formed by the bioelectric current sources in a region under examination of an examinee, with a plurality of magnetic sensors arranged adjacent the region under examination; PA1 a lattice point setting step for setting a plurality of lattice points in the region under examination, the lattice points being smaller in number than the magnetic sensors; PA1 a first current source computing step for deriving unknown current sources by adding a condition to minimize a square error of a magnetic field formed by an unknown current source at each of the lattice points and a magnetic field measured by each of the magnetic sensors; PA1 a checking step for checking whether the square error of the magnetic field computed from the current source derived and the magnetic field actual measured by each of the magnetic sensors is a global minimum; PA1 a lattice point rearranging step for moving the lattice points toward a lattice point having a large current value among the current sources computed at the first current source computing step, when the square error is determined to differ from the global minimum; PA1 a current source identifying step for repeating the first current source computing step to the lattice point rearranging step, and regarding as a true current source the current source corresponding to a magnetic field occurring when the square error is determined to be a global minimum at the checking step.
The orientatins and sizes of the current sources VPj on the respective lattice points are deduced by solving the above equation (5). The current source having the greatest value thereamong is regarded as the closest to a true current source. This is the principle of the current source deducing method based on the least norm method.
In order to improve the position resolving power of the least norm method, proposals have been made to gain least norm solutions repeatedly while subdividing the lattice points (see, for example, Y. Okada, J. Huang and C. Xu, 8th International Conference on Biomagnetism, Munster, August 1991). This method will be described briefly with reference to FIG. 2.
FIG. 2 is an enlarged view of part of the lattice points N shown in FIG. 1. Reference J in FIG. 2 denotes the lattice point having the current source deduced by the above least norm method as being close to the true current source. A group of subdivided lattice points M (shown in small black spots in FIG. 2) is additionally established around this lattice point J. The technique described above is applied to the newly established group of lattice points M as included in the initially established group of lattice points N, to deduce a current source still closer to the true current source.
The prior art described above has the following disadvantage.
The conventional method illustrated in FIG. 2 involves an increased number of lattice points since the subdivided lattice points M are newly established in addition to the initially established lattice points N. Consequently, vector [P] in equation (5) has a large number of elements which lowers the precision in computing the least norm solutions.